Differentiate cos−1⁡sin⁡x+cos⁡x2 with respect to x is

Use the formula cos ⁡acos ⁡b+sin ⁡asin⁡ b=cos ⁡(a−b)  and cos−1⁡(cos⁡x)=x tosimplify cos−1⁡sin⁡x+cos⁡x2 and then differentiate  w.r.t.x.Let,y=cos−1⁡cos⁡x+cos⁡x2y=cos−1⁡cos⁡x12+sin⁡x12=cos−1⁡cos⁡xcos⁡π4+sin⁡xsin⁡xπ4∵sin⁡π4=cos⁡π4=12y=cos−1⁡cos⁡x−π4[∵cos⁡(A−B)=cos⁡Acos⁡B+sin⁡Asin⁡B]Here , −π4